Functional Time Series Analysis Using Single-Index L1-Modal Regression

A new predictor in functional time series (FTS ) is considered. It is based on the asymmetric weighting function of quantile regression. More precisely, we assume that FTS is generated from a single-index model that permits the observation of endogenous–exogenous variables by combining the nonparametric model with a linear one. In parallel, the L1-modal predictor is estimated using the M-estimation of the derivative of the conditional quantile of the generated FTS. In the mathematical part, we prove the complete convergence of the constructed estimator, and we determine its convergence rate. An empirical analysis is performed to prove the applicability of the estimator and to evaluate the impact of different structures involved in the smoothing approach. This analysis is carried out using simulated and real data. Finally, the regressive nature of the constructed predictor allows it to provide a robust instantaneous predictor for environmental data.